1. Field of the Invention
The present invention generally relates to an apparatus and method for measuring the speed of a moving object, and in particular, to an apparatus and method for measuring the speed of these moving objects based on a roll angle.
2. Description of the Related Art
Generally, moving objects such as vehicles, ships, and aircrafts have an embedded navigation system that determines the position of the moving object (positioning), routes a path to a given destination (routing), and provides the routing results.
In order to determine the position of a moving object and provide a path to the destination, navigation systems should be able to determine the exact position of a vehicle. Therefore, navigation systems generally include a positioning device for position determination. Such positioning devices are classified into two types, one for determining the position using an outside source and the other for determining the position using an inside sensor. A Global Positioning System (GPS) is an example of the former type of positioning device. A Dead Reckoning (DR) system using an inertial sensor is an example of the latter type of positioning device.
A DR system calculates the speed and position of a moving object using a gyroscope for detecting a rotational motion of the moving object and an accelerometer for detecting a straight-line motion of the moving object. In particular, the speed of the moving object can be calculated using both speed information acquired from an acceleration measured by the accelerometer and moving direction information acquired from the gyroscope.
In general, the DR system measures the moving direction angle of a vehicle on a road and an acceleration in the moving direction of the vehicle, as well as calculates the moving speed vector of the vehicle using the moving direction angle of the vehicle and the acceleration in the moving direction of the vehicle. In order to measure the moving direction of the vehicle, the DR system requires a gyroscope installed on an axis perpendicular to a plane on which wheel axles (axis of axles) are placed and In order to measure the acceleration in the moving direction of the vehicle, the DR system requires the measurement value of a road inclination angle in addition to an accelerometer installed in the direction of the wheel axle (axis of axle).
The road inclination angle measurement value is required because a specific force component proportional to gravitational acceleration is included in the output of the accelerometer and the specific force component may be calculated from the road inclination angle. Since gravitational acceleration works perpendicularly to the surface of the earth spheroid (a spherical surface perpendicular to the directions of the gravitational acceleration) at all times, the angle of the axis of the accelerometer mounted in the vehicle (fixed in a particular direction within the vehicle) with respect to the surface of the earth spheroid changes, thereby resulting in a change in the specific force component included in the output of the accelerometer.
In other words, if the road inclination angle changes, the direction of the axis of the accelerometer mounted in the vehicle is not perpendicular to the direction of gravitational acceleration. Thus, the accelerometer measures a rate of change in the actual speed of motion (an actual motional acceleration) including a component of gravitational acceleration.
FIG. 1 is a view explaining a component of the gravitational acceleration included in the acceleration of a moving object. Referring to FIG. 1, a road inclination angle is inclined with respect to a plane perpendicular to the direction (±g) of the gravitational acceleration. In FIG. 1, an angle between a plane 20 perpendicular to the direction (±g) of the gravitational acceleration and a plane 10 extending in the moving direction of a vehicle 30 is a road inclination angle θ. When the vehicle 30 travels on the plane 10 inclined at the road inclination angle θ with respect to the plane 10 perpendicular to the direction (±g) of the gravitational acceleration as shown in FIG. 1, a measurement value {right arrow over (a)} of an accelerometer mounted in the vehicle 30 includes an actual acceleration and a component of a gravitational acceleration {right arrow over (g)}. Thus, the component of the gravitational acceleration {right arrow over (g)} is also measured together with a rate of change in the actual speed of motion and may cause a big error in the measurement of speed.
Thus, for accurate speed measurement, a vehicle DR system must subtract the gravitational acceleration {right arrow over (g)} from the measurement value {right arrow over (a)} of the accelerometer and measures the road inclination angle θ to measure the gravitational acceleration {right arrow over (g)}.
The DR system for vehicles can measure the road inclination angle θ using a rotational angle with respect to the forward direction of a vehicle, a rotational angle with respect to the lateral direction of the vehicle perpendicular to the forward direction of the vehicle, and a rotational angle and a roll angle φ with respect to the lower direction of the vehicle perpendicular to the forward direction and the lateral direction of the vehicle. The roll angle φ means the amount of inclination of the vehicle with respect to the forward direction of the vehicle.
FIG. 2 illustrates coordinate axes defined in a moving object. In FIGS. 2A and 2B, an axis along the forward direction of a vehicle is defined as an X axis, an axis perpendicular to the X axis and passing through the lateral sides of the vehicle is defined as a Y axis, and an axis perpendicular to an XY plane along the lower direction of the vehicle is defined as a Z axis.
Referring to FIG. 2, a rate of change in the road inclination angle θ can be expressed in Equation (1) as follows:
                                          E            θ                    =                                                    ω                Y                            ⁢              cos              ⁢                                                          ⁢              ϕ                        -                                          ω                Z                            ⁢              sin              ⁢                                                          ⁢              ϕ                                      ,                            (        1        )            
where ωY is an angular speed along the Y axis, ωZ is an angular speed along the Z axis, and φ is the roll angle of the vehicle. At this time, the roll angle φ means the angle of inclination of the vehicle along the X axis.
The change rate of the roll angle φ can be expressed in Equation (2) as follows:
                                          E            ϕ                    =                                    ω              X                        +                                          ω                Y                            ⁢              sin              ⁢                                                          ⁢              ϕtanθ                        -                                          ω                Z                            ⁢              cos              ⁢                                                          ⁢              ϕtan              ⁢                                                          ⁢              θ                                      ,                            (        2        )            
where ωX is an angular speed along the X axis. Equations (1) and (2) are well-known relational expressions related to the change rate of an Euler angle.
Referring to Equation (2), to accurately calculate the change rate
  E  ϕof the roll angle φ, three axis gyroscopes are required for measuring the angular speed ωX along the X axis, the angular speed ωY along the Y axis, and the angular speed ωZ along the Z axis.
However, generally, a roll motion that is a rotational motion with respect to a wheel axle (axis of axle) (the X axis) connecting the front and rear sides of the vehicle and a straight line motion with respect to an axis (the Z axis) perpendicular to the ground surface is negligible during driving of the vehicle. Thus, conventionally, the road inclination angle θ is calculated only using the angular speed ωX along the X axis and the angular speed ωY along the Y axis, irrespective of the roll angle φ and the angular speed ωZ along the Z axis in Equation (2).
When the roll angle φ and the angular speed ωZ along the Z axis are neglected, i.e., they are assumed to be 0, Equation (1) is
      E    θ    =                    ω        r            ⁢      cos      ⁢                          ⁢      θ        -          θ      ⁢                          ⁢      E      ⁢                          ⁢      sin      ⁢                          ⁢      θ      and the change rate
                                          E            θ                    =                      ω            r                          ,                            (        3        )            of the roll angle φ can be given as in Equation (3) by:
  E  ϕ
where ωr can be calculated from the output of a gyroscope that measures an angular speed along an axis (the Y axis) passing through the lateral sides perpendicular to the forward direction of the vehicle and the road inclination angle θ is obtained by integrating ωr.
However, when there are many curves on the road and thus the roll angle of the vehicle increases, the roll angle of the vehicle has a significant influence upon the road inclination angle. In addition, when the angular speed ωZ along the Z axis is large in Equation (1), even if the roll angle of the vehicle is not large, the roll angle of the vehicle has a significant influence upon the road inclination angle. As a result, a conventional calculation of the road inclination angle θ, which neglects the roll angle of the vehicle, has a significant error.
In other words, in the case where the roll angle of the vehicle has a large influence upon the road inclination angle, the road inclination angle calculated using Equation (3) neglecting the roll angle of the vehicle has a difference with the actual road inclination angle, which increases over time. As a result, there are large differences between measured speed and position and actual speed and position. Thus, the road inclination angle should be calculated based on the roll angle of the vehicle.
In Equation (2), gyroscopes for the X axis, the Y axis, and the Z axis are required to calculate the change rate
  E  ϕof the roll angle φ based on the roll angle
φ. However, to use the gyroscope for three axes, additional gyroscopes must be mounted in a DR system, increasing the manufacturing cost of the DR system for measuring the speed of the vehicle.